Granular Mechanics of the Seismic Lateral Earth Pressure on Rigid Retaining Walls

Abstract eng:
Small scale experiments, ran by different authors on the seismic behavior of retaining walls, have led to the conclusion that the distribution of the active lateral soil pressure exhibits a nonlinear tendency, and is highly dependent on the kinematics of the wall; despite of the assumptions of the Mononobe-Okabe method. In this paper, both of these features are explained in a direct and simple way by means of the Granular Mechanics, whose principal hypothesis is the transmission of stresses as chains of forces of contact between grains, which has been experimentally confirmed by the photographs taken on packings of birefringent disks. Previously, by applying the principle of the mean value, it is demonstrated that any function in a disordered discontinuum can be attained as it were in a crystalline substance, whose cell parameters are defined by the variances and covariances of the original fabric metrics. Regarding this result, the random chains of contact forces, inherent to dense soils, are treated as they were linear, conjugate and ordered. When they are associated to their geometric domain of influence, chains come to be bands of contact forces, The pseudo-statics of these bands provides the stresses for a linearly bounded soil mass, in “at rest” condition, or Rankine´s plastic state. A shear band shows up if only one band of contact forces reaches the plastic state. This is the case of the backfill at limit equilibrium, where a plastic band separates the mobilized wedge from the unstrained soil. On this basis, by applying just the law of sines to the quantities involved, a general bilinear equation for the seismic earth lateral pressure is deduced, which may be specialized for the three elementary movements of the rigid wall: rotation about the base, horizontal translation, and rotation about the top. The kinematics of the grains in the rhomboid cell, relative to the movement mode, defines the inclination of the contact forces, and, hence, the inclination of the respective band. In the first mode of movement, the pressure distribution is linear, but the lateral force resultant is larger than the Monobe-Okabe´s. In the second and third modes, the earth pressure distribution is bilinear with the maximum value near the base and near the top, respectively. In the third mode, the bands inclined toward the back side of the retaining wall are deduced to be in passive plastic state. For rotating walls, two modes of inter-grains movements are possible, giving rise to a semi-plastic state and a full plastic state of the soil mass, that, regarding the energy involved, are related to moderate and severe earthquakes, respectively. Finally, the lateral earth pressure and the resultant force, obtained in this theory, are compared with the published experimental data, showing a good agreement.

• Export as: BibTeX | MARC | MARCXML | DC | EndNote | NLM | RefWorks
• Add to your basket